The role of local spatial heterogeneity in the maintenance of parapatric boundaries: agent based models of competition between two parasitic ticks

Recent models of ecological parapatry, where the geographical distributions of two similar species abut without overlapping, have shown that spatial gradients in intrinsic growth rates can lead to sharp boundaries when dispersal is density dependent. However, a well documented parapatric boundary in southern Australia between two tick species that parasitise a large lizard lacks one or both of these features; dispersal of ticks is random and there may not be a gradient of population growth rates for one of the species. There is local variation in population growth rates arising from variation in the number of host lizards with overlapping host ranges. When more hosts are available there is a shorter waiting time for a host to arrive, and consequently higher survival rates. We construct a spatially explicit agent based model of the interaction between the two ticks and their lizard host and explore the role that this fine scale spatial heterogeneity plays in maintaining the parapatric boundary between the two tick species geographic distributions.